We study the following problem: given an integer k≥3 and a simple graph G, sample a connected induced k-node subgraph of G uniformly at random. This is a fundamental graph mining primitive with applications in social network analysis, bioinformatics, and more. Surprisingly, no efficient algorithm is known for uniform sampling; the only somewhat efficient algorithms available yield samples that are only approximately uniform, with running times that are unclear or suboptimal. In this work we provide: (i) a near-optimal mixing time bound for a well-known random walk technique, (ii) the first efficient algorithm for truly uniform graphlet sampling, and (iii) the first sublinear-time algorithm for ϵ-uniform graphlet sampling.
@article{arxiv.2007.12102,
title = {Efficient and near-optimal algorithms for sampling small connected subgraphs},
author = {Marco Bressan},
journal= {arXiv preprint arXiv:2007.12102},
year = {2021}
}